Summary: An infinitesimal, orthotropic theory of viscoplasticity based on overstress for thermomechanical loading is presented. The total strain rate is the sum of elastic, inelastic and thermal strain rates. An orthotropic constitutive law is postulated for each strain rate using the characteristics of orthotropic matrices and previous isotropic formulations of the viscoplasticity theory as a guide. All material functions and constants can be functions of current temperature and no influence of temperature history is modeled. Yield surfaces and loading/unloading conditions are not used in the theory in which the inelastic strain rate is solely a function of the overstress, the difference between stress and the equilibrium stress, a state variable of the theory. A comparatively simple theory is obtained which is capable of modeling important phenomena like creep, relaxation, rate sensitivity, hysteresis, tension/compression asymmetry and nearly elastic regions. It is also possible to model quasielastic behavior in one direction while the others behave viscoplastically. The theory is shown to reduce to a previously proposed formulation for inelastic incompressibility and isotropy.